Radiative-conductive heat transfer in a semitransparent composite with microspherical particles

A mathematical model for calculating the temperature field in a semitransparent composite material that includes a polymethyl methacrylate matrix and quartz microspheres is suggested. In calculating the optical properties of the composite material, use was made of the optical properties of the matrix and of the interacting quartz microspheres at different filling factors which characterize the volume concentration of particles in the matrix. Allowance for the interaction between the composite components is made following the Maxwell–Garnett approximation. Data on the complex refractive index of the composite were used for calculating the coefficients of absorption, scattering, and attenuation of packed particles by the Mie theory. The temperature fields in a layer of the material are found from solving the boundary-value problem for the energy equation and a system of radiation transfer equations with the use of these coefficients.